/**
* Problem 13 - Large sum
* @see {@link https://projecteuler.net/problem=13}
*
* Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.
*
* @author ddaniel27
 */
package problem13

var numbers = [100]string{
	"37107287533902102798797998220837590246510135740250",
	"46376937677490009712648124896970078050417018260538",
	"74324986199524741059474233309513058123726617309629",
	"91942213363574161572522430563301811072406154908250",
	"23067588207539346171171980310421047513778063246676",
	"89261670696623633820136378418383684178734361726757",
	"28112879812849979408065481931592621691275889832738",
	"44274228917432520321923589422876796487670272189318",
	"47451445736001306439091167216856844588711603153276",
	"70386486105843025439939619828917593665686757934951",
	"62176457141856560629502157223196586755079324193331",
	"64906352462741904929101432445813822663347944758178",
	"92575867718337217661963751590579239728245598838407",
	"58203565325359399008402633568948830189458628227828",
	"80181199384826282014278194139940567587151170094390",
	"35398664372827112653829987240784473053190104293586",
	"86515506006295864861532075273371959191420517255829",
	"71693888707715466499115593487603532921714970056938",
	"54370070576826684624621495650076471787294438377604",
	"53282654108756828443191190634694037855217779295145",
	"36123272525000296071075082563815656710885258350721",
	"45876576172410976447339110607218265236877223636045",
	"17423706905851860660448207621209813287860733969412",
	"81142660418086830619328460811191061556940512689692",
	"51934325451728388641918047049293215058642563049483",
	"62467221648435076201727918039944693004732956340691",
	"15732444386908125794514089057706229429197107928209",
	"55037687525678773091862540744969844508330393682126",
	"18336384825330154686196124348767681297534375946515",
	"80386287592878490201521685554828717201219257766954",
	"78182833757993103614740356856449095527097864797581",
	"16726320100436897842553539920931837441497806860984",
	"48403098129077791799088218795327364475675590848030",
	"87086987551392711854517078544161852424320693150332",
	"59959406895756536782107074926966537676326235447210",
	"69793950679652694742597709739166693763042633987085",
	"41052684708299085211399427365734116182760315001271",
	"65378607361501080857009149939512557028198746004375",
	"35829035317434717326932123578154982629742552737307",
	"94953759765105305946966067683156574377167401875275",
	"88902802571733229619176668713819931811048770190271",
	"25267680276078003013678680992525463401061632866526",
	"36270218540497705585629946580636237993140746255962",
	"24074486908231174977792365466257246923322810917141",
	"91430288197103288597806669760892938638285025333403",
	"34413065578016127815921815005561868836468420090470",
	"23053081172816430487623791969842487255036638784583",
	"11487696932154902810424020138335124462181441773470",
	"63783299490636259666498587618221225225512486764533",
	"67720186971698544312419572409913959008952310058822",
	"95548255300263520781532296796249481641953868218774",
	"76085327132285723110424803456124867697064507995236",
	"37774242535411291684276865538926205024910326572967",
	"23701913275725675285653248258265463092207058596522",
	"29798860272258331913126375147341994889534765745501",
	"18495701454879288984856827726077713721403798879715",
	"38298203783031473527721580348144513491373226651381",
	"34829543829199918180278916522431027392251122869539",
	"40957953066405232632538044100059654939159879593635",
	"29746152185502371307642255121183693803580388584903",
	"41698116222072977186158236678424689157993532961922",
	"62467957194401269043877107275048102390895523597457",
	"23189706772547915061505504953922979530901129967519",
	"86188088225875314529584099251203829009407770775672",
	"11306739708304724483816533873502340845647058077308",
	"82959174767140363198008187129011875491310547126581",
	"97623331044818386269515456334926366572897563400500",
	"42846280183517070527831839425882145521227251250327",
	"55121603546981200581762165212827652751691296897789",
	"32238195734329339946437501907836945765883352399886",
	"75506164965184775180738168837861091527357929701337",
	"62177842752192623401942399639168044983993173312731",
	"32924185707147349566916674687634660915035914677504",
	"99518671430235219628894890102423325116913619626622",
	"73267460800591547471830798392868535206946944540724",
	"76841822524674417161514036427982273348055556214818",
	"97142617910342598647204516893989422179826088076852",
	"87783646182799346313767754307809363333018982642090",
	"10848802521674670883215120185883543223812876952786",
	"71329612474782464538636993009049310363619763878039",
	"62184073572399794223406235393808339651327408011116",
	"66627891981488087797941876876144230030984490851411",
	"60661826293682836764744779239180335110989069790714",
	"85786944089552990653640447425576083659976645795096",
	"66024396409905389607120198219976047599490197230297",
	"64913982680032973156037120041377903785566085089252",
	"16730939319872750275468906903707539413042652315011",
	"94809377245048795150954100921645863754710598436791",
	"78639167021187492431995700641917969777599028300699",
	"15368713711936614952811305876380278410754449733078",
	"40789923115535562561142322423255033685442488917353",
	"44889911501440648020369068063960672322193204149535",
	"41503128880339536053299340368006977710650566631954",
	"81234880673210146739058568557934581403627822703280",
	"82616570773948327592232845941706525094512325230608",
	"22918802058777319719839450180888072429661980811197",
	"77158542502016545090413245809786882778948721859617",
	"72107838435069186155435662884062257473692284509516",
	"20849603980134001723930671666823555245252804609722",
	"53503534226472524250874054075591789781264330331690",
}

func Problem13() string {
	sum := "0"

	for _, n := range numbers {
		sum = add(sum, n)
	}

	return sum[:10]
}

func add(a, b string) string {
	if len(a) < len(b) {
		a, b = b, a
	}

	carry := 0
	sum := make([]byte, len(a)+1)

	for i := 0; i < len(a); i++ {
		d := int(a[len(a)-1-i] - '0')
		if i < len(b) {
			d += int(b[len(b)-1-i] - '0')
		}
		d += carry

		sum[len(sum)-1-i] = byte(d%10) + '0'
		carry = d / 10
	}

	if carry > 0 {
		sum[0] = byte(carry) + '0'
	} else {
		sum = sum[1:]
	}

	return string(sum)
}
